The transversal and longitudinal wave velocities, the acoustic attenuation coefficients, the nonlinear coefficients at different pressures and the acoustic attenuation coefficient as a function of frequency in a two-dimensional (2D) monodisperse disc system are numerically calculated. The results show that the transversal and longitudinal wave velocities both exhibit a piecewise power law with pressure P. When P -4, the velocity decreases with the increase of pressure in the 2D disc granular system, and when P > 10-4, the transversal wave velocity Vt and longitudinal wave velocity Vl show the scaling power laws, i.e., νt~P0.202 and vl~P0.338, respectively. The ratio of the shear modulus to the bulk modulus G/B shows a power law scaling with the pressure, G/B~P-0.502, implying that the system lies in an L glass state at low pressure, similar to that of a three-dimensional (3D) spherical granular system. The attenuation coefficients (αT, αL) of the horizontal excitation and vertical excitation also show the picecewise behaviors with the change of frequency f. When f f. When f > 0.05, α ∝ fTα, αL ∝ f. And when f > 0.35, αT ∝ f2 and αL ∝ f1.5. In addition, the nonlinear coefficient and the attenuation coefficient of the 2D disc granular system under the vertical and horizontal excitation both also show a piecewise law behavior with pressure, similar to that of the acoustic velocity. When P -4, only the transversal nonlinear coefficient changes according to βT ∝ P-0.230, while the other coefficient has no change. When P > 10-4, the attenuation coefficients and nonlinear coefficients decrease according to their power law with the increase of pressure, i.e., βT ∝ P-0.703, βL ∝ P-0.684, αT ∝ P-0.099, αL ∝ P-0.105. The characteristic length l*, which characterizes the disordered structure responsible for the scattering, also decreases according to power law with the increase of pressure, when P -4, l* ∝ P-0.595; when P > 10-4, l* ∝ P0.236.